{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 结构力学例题\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          4.99791753  9.7875885  14.36901291 18.74219075 22.90712203\n",
      " 26.86380675 30.6122449  34.15243648 37.48438151 40.60807997 43.52353186\n",
      " 46.23073719 48.72969596 51.02040816 53.1028738  54.97709288 56.64306539\n",
      " 58.10079134 59.35027072 60.39150354 61.2244898  61.84922949 62.26572262\n",
      " 62.47396918 62.47396918 62.26572262 61.84922949 61.2244898  60.39150354\n",
      " 59.35027072 58.10079134 56.64306539 54.97709288 53.1028738  51.02040816\n",
      " 48.72969596 46.23073719 43.52353186 40.60807997 37.48438151 34.15243648\n",
      " 30.6122449  26.86380675 22.90712203 18.74219075 14.36901291  9.7875885\n",
      "  4.99791753  0.        ]\n",
      "[ 50.          47.95918367  45.91836735  43.87755102  41.83673469\n",
      "  39.79591837  37.75510204  35.71428571  33.67346939  31.63265306\n",
      "  29.59183673  27.55102041  25.51020408  23.46938776  21.42857143\n",
      "  19.3877551   17.34693878  15.30612245  13.26530612  11.2244898\n",
      "   9.18367347   7.14285714   5.10204082   3.06122449   1.02040816\n",
      "  -1.02040816  -3.06122449  -5.10204082  -7.14285714  -9.18367347\n",
      " -11.2244898  -13.26530612 -15.30612245 -17.34693878 -19.3877551\n",
      " -21.42857143 -23.46938776 -25.51020408 -27.55102041 -29.59183673\n",
      " -31.63265306 -33.67346939 -35.71428571 -37.75510204 -39.79591837\n",
      " -41.83673469 -43.87755102 -45.91836735 -47.95918367 -50.        ]\n"
     ]
    }
   ],
   "source": [
    "l=5\n",
    "q=20\n",
    "x=np.linspace(0,l,50)\n",
    "M=q/2*(l*x-x**2)\n",
    "V=q*(l/2-x)\n",
    "print(M)\n",
    "print(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pbX0iIn1IAUtEBl79/pObUB8vBxMB4y9zYatwISSO8LpCEZFeUcASEW8d33kybNXvAxMJk65yYavgeohP9bpCEZFzpoAlIqHBWqjefjJsNR6CyBiYPNeFrfxrIXaY11WKiJwVdXIXkdBgDIya5m5zvw1HNgfD1nLXbysqHvLmuz5bufMhOt7rikVE3heNYImI9wIBqNrgwlb5CmirhZhhbkSr5GaYNAeiYr2uUkTkbTRFKCKDh98HlS+7sLVzFXScgNgUKLzB9diacAVERntdpYiIApaIDFL+HjjwgtuqZ9fj0NUM8Wmu5UPJEhh3KUREel2liIQprcESkcEpMhpy57lbTyfsf9aNbG1/BDb/AYZlQtFiF7bGXgAREV5XLCICDMAIljHmGuDnQCTwO2vtD9/tsRrBEpGz0t0Oe592I1t7ngF/FySPcZ3jS5bA6PO0CbWI9DvPpgiNMZHAHmAecBh4HbjVWlt+uscrYInIOetsht1PurYP+56FQI/bC/HNfREzSxS2RKRfeDlFeAGwz1p7IFjIX4FFwGkDVn8LBCzz7/wNHTvWEN3V6EUJItKPhkUVcHl6E1eNrGdmwz1EvnwPlW2xPF87nOeOD+dQe5zXJYrIAGhNL2JCzlj+ds+3PKuhvwPWGKDqlM8PAxee+gBjzO3A7QA5OTn9WszhEx0cihyNr+RjZOxdSXxz1Xt/kYgMGq2+KJ6sHsGT1SNIie7hiowmrso4wcfHVfOP46vZ1xrH88eH8/zx4RztVNsHkaHGAo3Zl9M05iIi/bVYazEejWD3d8A63d/qbXOS1tp7gXvBTRH2ZzE5IxJYc+d8bvvTJipib+X7i0v48AX9G+pEJAQ0H4PylUwuW8bkYRv59MRjMHqGm0YsvglSs72uUER6qa3Lx/97eCvPlNdw6wU5fHfRtZ6FK+j/NVgXA9+21i4Ifv5NAGvtD073+IFag9Xc2cMXHnqDF/fU8qlLJ3DX9YVERmiNhkhYaKxynePLlsHRN9yx7AuDYWsxJGV5W5+InLOjjR380582sau6mX+7oYh/vGT8gIQrLxe5R+EWuV8NHMEtcv+ItbbsdI8fyEXuPn+A/3xiF/e9cpAr8zP45a0zSIpT80KRsNJw4ORWPTWlgIHxl7lRraJFkJjudYUi8h62HDrB7fdvpqvHzy8/MoMr80cO2Gt72mjUGHMd8DNcm4b7rLV3v9tjvbiK8MGNlfzHyjImpCfy+0+cT86IhAF9fREJEbW7T25CXbcHTCRMvMKNbBXeAPHDva5QRN5h5dYjfO3R7WQlx/H7T8wiNzNpQF9fndzfw6v76vjnB7cQGWH47cdmcsGEtAGvQURChLVQU+aCVulSOFEBEdEw+WoXtgqug9iB/SEuIm8XCFh+tnYPv3huHxdMSOO3H5tJWmLMgNehgHUWDta1cdufXqeqoZ27b5rCLbO06FUk7Fnr1mmVLYPS5dB8GKLiXGf5kpshdwHEaNRbZCC1d/v46iPbeLK0mltmjeX7i6cQE+XNLg4KWGepqaOHf3loCy/treP22RP5+jUFWvwuIk4gAIdfd6Na5SugtQaiEyH/WtfQdPJciFLrB5H+VN3UyT/d/zplR5u567pCbrtsgrdXCipgnT2fP8B3V5dz//pK5hSM5Gcfnk6yFr+LyKkCfqh8xa3ZKl8JHQ0QmwwFN7iwNfFKt4+iiPSZNw6d4DN/3kxbl49ffmQGcwoyvS5JAev9+PP6Cr7zWDk5IxK49x9mMXnkMK9LEpFQ5O+Bgy+6sLVzNXQ1uQXxhQtd2Bp/OUREel2lyKD28OuH+LcVZWSmxPJ/H59FQVay1yUBCljv28YD9Xz+oS109gS455ZpzC9WfxwROQNfF+x/zoWt3U9AdyskZkDRYhe2si+CCG/WiogMRt2+AN9dXcYDGw5xeW46v7x1BqkJA7+Y/d0oYPXC0cYO/vmBzWw73MSXrs7lS1fnEqF1WSLyXno6YO8zLmzteRp8HZA02vXYKlkCY2ZqE2qRMzje0snnHtjCpsoTfOaKidy5IPTWRStg9VJnj59/XVHKo5sPM7cwk3s+NE3rskTk7HW1wp6nXNjatwb83ZCa49o+lCyBrKkKWyKneOPQCf75gS00dfTw4w9M5cZpo70u6bQUsPqAtZb711fyvdValyUivdDR6KYPS5fBgech4IMRk4Nh62YYWeB1hSKeeuT1Kv51RSmZKbH878dmUTQ6NNZbnY4CVh/aeKCezz24hS5fgP/+0HTmFXl/FYOIDFLtDbBzlWv9UPEy2ACMLHKjWsVLYMQkrysUGTDdvgDfW13OnzdUcnluOr/48AyGe9A89FwoYPWxo40dfPaBzWw/3MSX5+byxTlalyUivdRS41o+lC2DQ+vdsVHT3KhW8U1uSlFkiKpt6eJzD27m9YoTfGb2RL62IJ+oyNC/IEQBqx909vi5a3kpS7e4dVk/vWUaKfFalyUifaDpMJStcCNbR7e4Y2PPd2GraDEkj/K2PpE+9OZ6q8aObn78gWksDNH1VqejgNVPrLX86dUKvv/4TsYMj+c3Hz2P4tEpXpclIkNJw0EoW+5Gtqp3AAbGXeJGtYoWw7AMrysUeV/e/B169xM7yUyO495/CO31VqejgNXPNlc28PkH36ChvZvvLSrmQ+drKF9E+kHdXrc4vnQp1O0GEwETZrv1WoU3QoI2qpfBobXLxzeWbmf19mNcXTCSe26ZTkrC4JsFUsAaAHWtXXz5r1t5eV8dH5w5lu8uKiE+Rt2bRaQfWAvHy13YKlsGDQcgIgomzXFhq+A6iNNouoSmPTUtfPaBzVTUtfG1BQV8ZvbEQbuOWQFrgPgDlp8/u5dfPreX/Mwk/udjM5mQnuh1WSIylFkLx7a5Ua2y5dBUBZGxkDvPTSPmXwsx+jkkoWH5G4f51rJSEmOj+OWtM7h40givS+oVBawB9sLu43z54a34/JaffGAq107RglQRGQDWwuFNJ8NWazVEJ0DeAjeylTsPouO9rlLCUGePn++uLuehjYe4YEIav7p1BiOT47wuq9cUsDxwpLGDzz+4ha1Vjdx22QS+cW0B0YPgklMRGSICftfuoXQZlK+A9nqISXLTh8VL3HRiVGj3GJKhoaqhnc89uIUdR5r47BWTuGN+3qBowXA2FLA80u0L8J9P7OSPr1Ywc9xwfvWRGYxK0btHERlgfh9UrHNha+cq6GyCuFQovMG1fhg/GyKjvK5ShqC15TV85ZGtANxzy3TmDrHm3ApYHlu9/Shff3Q7sdGR/OxD05mdp8uqRcQjvm63RU/pUtj1BHS3QEI6FC1yHeRzLoYIXaAjvdPjD/DTZ/bw2xf3UzImmd98ZCY5IxK8LqvPKWCFgP21rXzugS3srmnhM1dM5Kvz8omJGhpDpCIySPV0wL61LmzteRp62mFYllscX7LENTfVJtRyjqoa2vniX9/gjUONfOTCHP79hiLioodmaFfAChGdPX6+t7qcBzceYlp2Kr/88IwhmehFZBDqboM9T7lpxL1rwN8FKdknw9ao6Qpb8p4e336MbyzbDsAPl0zl+qlD+yIvBawQ8+SOY3x96XashbuXTBlU2wKISBjobIbdT7iwtf9ZCPggbaJbHF+yxG1IrbAlp+jo9vPd1WX85bUqpmen8stbZ5CdNvQHEBSwQtDhE+186a9b2Vx5gltmjeXbC4tJiNEiUxEJMe0NsGu1m0Y8uA5sADIKToat9FyvKxSP7apu5gsPvcG+2lY+e8UkvjIvL2yumlfAClE+f4Cfrd3Lr1/Yx8T0RH71kfMoHDW49mESkTDSehzKV7oeW5WvAhYyp7igVbIEho/3ukIZQNZaHth4iO+vLicpLpr//tA0Ls8Nr4u4FLBC3Kv76vjyw1tp7OjhX68v5B8uGofR8LuIhLLmo1C2wm3Vc/h1d2zMTDeyVXwTpIzxtj7pV03tPXx96XaeKqtmdl4GP/3gNDKSYr0ua8ApYA0C9a1d3PG3bTy/u5Z5RZn85ANTSU1QE0ARGQROVLpRrbJlbtsecO0eipe49g9JQ6v3UbjbVNHAl/66lZrmTu68Jp9/umzw7iXYW/0WsIwxPwFuBLqB/cAnrbWNwfu+CdwG+IEvWmuffq/nC+eABRAIWO575SA/emoXIxJj+a8PTuOy3HSvyxIROXv1+09uQn28HEwEjL/sZNhKSPO6QnmfevwBfvncPn79/D7GpMbzi1tnMD071euyPNWfAWs+8Jy11meM+RGAtfbrxpgi4C/ABcBoYC2QZ631n+n5wj1gvWnH4Sa+9PAbHKht45OXjufr1xQM2R4iIjKEHd/pwlbpUmjYDxFRMPFKF7YKrof48P7lPJjsr23lKw9vZdvhJpbMGMN3FhWTFBftdVmeG5ApQmPMTcAHrLUfDY5eYa39QfC+p4FvW2vXn+k5FLBO6uj286OndvHHVyvIHTmM//7QdErGpHhdlojIubMWqrefHNlqPASRMTB5rgtb+ddC7DCvq5TTsNbywIZK7n5iJ3HRkdy9eMqQ7211LgYqYD0GPGytfcAY8ytgg7X2geB9vweetNY+epqvux24HSAnJ2dmZWVln9QzVKzbU8vXHt1GQ1s3X56bx2evmERkmM51i8gQYC0c2XwybLUcg6h4yJvv9kXMnQ/R2rM1FBxv7uRrj27nxT21zM7L4CcfmEpmcpzXZYWUXgUsY8xaIOs0d91lrV0ZfMxdwCxgibXWGmN+Dax/R8B6wlq79EyvpRGs02ts7+au5aU8vuMYs8YN578/ND0sGriJyBAXCEDVBjeFWL4S2mohZpgb0SpeApOvhqjwuzItFDy54xjfXL6Dzh4/37pOV7e/m34dwTLGfAL4LHC1tbY9eExThH3MWsvKrUf5t5WlBAKW/1hYzAdnjtV/eBEZGvw+qHzZha2dj0HHCYhNgcIbXI+tCVdApNb89Lfmzh6+vaqMZVuOMHVsCvfcMp3JIzV9+276c5H7NcA9wBXW2tpTjhcDD3FykfuzQK4WuffekcYO7nhkG+sP1DO/KJMfLJnCiGF6hyciQ4ivGw6+6MLWrsehqxni09xViCVLYNylEKELf/raxgP1fOWRbVQ3d/L5qybzhTmTw6Yj+/vVnwFrHxAL1AcPbbDWfjZ4313ApwAf8GVr7ZPv9XwKWGfnzXYOP35qN8nx0dx9UwkLik83iysiMsj1dLr9EEuXwu4noacdhmVC0WIXtsZeABEKAb3R2ePnp8/s5ncvH2RcWgL3fGg65+UM97qsQUGNRoeoXdXNfOXhbZQfa+bGaaP5zsJi0hLVnFREhqjudtj7tAtbe9eArxOSx0JxMGyNPk+bUJ+j1ysauPPR7Rysa+OjF+bwresKSYzVvrhnSwFrCOvxB/jtC/v5xXN7SY6L5nuLS7huii6hFZEhrqvFjWiVLoV9z0Kgx+2F+OYm1JklCltn0N7t4ydP7+aPr1YwJjWeH988lUsmq7H1uVLACgO7qpv52t+2s+NIE9dNyeK7i0pI19osEQkHHSdg52rX9uHAi2D9kJ53Mmxl5HtdYUjZcKCery/dTmV9O5+4eBx3XlOgUav3SQErTPj8Ae596QA/W7OXxNhIvrOohBunjtKVhiISPtrqXMuHsuVQ8TJg3WhW8U0ubKVN9LpCz7R1+fjRU7u4f30l40Yk8KObp3LRxBFelzWoKWCFmb01LXzt0e1srWpkflEm37+phJFJag4nImGm+VgwbC2Dqo3u2OgZbmSr+CZIzfa2vgH06r467ly6nSONHXzykgncsSCPhBiNWvWWAlYY8gcsv3/5AP/1zB7ioyP59sIiFk8fo9EsEQlPjYegbIVbs3VsqzuWfaHrHl+0CJKG5pXYLZ09/ODJXTy08RAT0hP5yQemMmu8NtzuKwpYYWx/bSt3PrqdzZUnuCo/g+8uKlEXeBEJb/X73RRi6TI4XgYYGH+Zm0IsXASJQ2PabG15Df++spTq5k7+6fKJfGVeHnHR6h/WlxSwwpw/YPnTqxX81zO7sRb+37xcPnXpBKLUQE5Ewl3tbhe0SpdC/V4wkTDxShe2Cm6A+FSvKzxn1U2dfHtVGU+VVZOfmcQPbp6ivlb9RAFLADja2MG/ryxj7c4aCkcl84MlUz0H5V8AABq1SURBVJiePfh+eIiI9DlroabUBa3SZdBYCRHRMHmuC1v510JsktdVnpE/YHlgQyU/eXo3Pf4AX5qby6cvn6hu7P1IAUve5qnSar69qoyalk4+ftE47liQT1Kc9vgSEQFc2Dq6xQWtsuXQfASi4iB3nluzlbsAYkJrqUX50Wa+uXwH26oauTw3nbsXTyFnRGjVOBQpYMnfaens4afP7OFP6ysYmRTLdxYWs6A4S4vgRUROFQjA4dfcyFbZCmg7DtGJkH+NC1uT50KUdz0H27t9/HztXn738kGGJ0TzbzcUsXDaaP0sHyAKWPKutlY18q1lOyg/1szcwpF8Z1EJY1LjvS5LRCT0BPxQ+YoLW+WroKMBYpOh4HoXtiZeCZEDNxvw/K7j/OuKUo40dnDrBdl8/ZoCUhO0XdpAUsCSM/L5A/zhlQruWbMHY+Ar8/L4xCXjNW8vIvJu/D2ua3zZMtdFvqsJ4odD4UK3Zmv85RDRP1fsVTd18r3V5Ty+4xi5I4fxn0umcL5aL3hCAUvOSlVDO/++spTnd9eSO3IY31lYrL2pRETei6/L7YdYtgx2PQE9bZA40vXXKlkC2RdBRO/fsHb7Avz+5YP88rm9+AKWL1w1mc9cMYmYKL0Z9ooClpw1ay1rdx7nu6vLqGro4Popo7jr+kJGa9pQROS9dbfD3mdc2NrzNPg6IWl0cKuem2HMee9rE+oX99TynVVlHKhrY15RJv92fZEWsYcABSw5Z509fu5dd4BfP7+PCGP4/FWT+KfLJ6pJnYjI2epqgd1PubC1by34uyF13MmwlTXlPcNWVUM7311dzpryGiakJ/IfNxZxZf7IAfoLyHtRwJL3raqhnbsf38lTZdWMG5HAf9xYxJyCTK/LEhEZXDoaYdfjLmztfx6sH0ZMdvsiltwMIwve/vBuP//z4n5+++J+oiIMX5iTy6cuG09slN7khhIFLOm1l/bW8u1VZeyvbWNOwUj+/YYixqcnel2WiMjg01YPO1e5sHXwJcDCyCIoXoItvomnq4fxvdXlHGnsYOG00XzrukKyUuK8rlpOQwFL+kS3L8CfXq3gZ2v30OO3fHr2BD535WQSY7Uju4jI+9JSA+UrXeuHqg0A7AiMZ2PClZx33W2cN3WqxwXKmShgSZ863tzJD57cxfI3jpCRFMtX5+XxwVnZREaosZ2IyLmqa+3iZ2v38MJrW1kU8xr/mLyZjOYyd+fY890UYtFiSB7lbaHydxSwpF9sOXSC768uZ8uhRvIzk/jW9YVckZfhdVkiIoNCZ4+f3798kP95YT8dPX4+dmEOX7w6lxHDYqHhoJtCLF0ONTsAA+MuhZKboHARDNPP2lCggCX9xlrLk6XV/PDJXRxqaGd2XgZ3XVdIflZob4oqIuKVQMCyattRfvL0bo40djC3MJNvXlfApIxhp/+Cur1uX8TSpVC3G0wkTJjtemwV3AAJajLqFQUs6XddPj9/Xl/JL57dS2uXj1tmZfOVeXmMTNbCTBGRN204UM/dj+9kx5EmSsYkc9d1RVw8acTZfbG1cLz8ZNg6cRAiomHSHBe28q+DuOT+/QvI2yhgyYBpbO/mF8/u488bKoiOjOAzsyfx6dkTSIjRQngRCV8Halv5wZO7WFNew6iUOO68Jp9F08YQ8X7XrloLx7ae3IS6qQoiYyF3ngtbeddAjK707m8KWDLgKura+NFTu3iytJrM5Fi+Mi+Pm88bS5T2NxSRMHK8pZNfP7ePBzceIjYqgs9dNZnbLpvQt02bAwE4sulk2GqthugEyFvgFshPngfRmk3oDwpY4pnXKxq4+/GdbK1qZGJ6Iv9vXh7XTxn1/t+1iYgMAk3tPfzvuv384ZUKuv0BPnx+Nl+em0dGUmz/vnDAD5WvugXy5SuhvR5ikqDgejeyNfEqiIrp3xrCSL8HLGPMHcBPgAxrbV3w2DeB2wA/8EVr7dPv9TwKWEOTtZY15TX89Jk97K5poXBUMnfMz2NOwUjM+9iTS0QkVLV1+fjDKwf533UHaO3ysXDaaL48N48JXjRm9vvg4IsubO18DDqbIC4VCm90YWv8bIjU8o3e6NeAZYzJBn4HFAAzrbV1xpgi4C/ABcBoYC2QZ631n+m5FLCGNn/A8ti2o/z32j1U1rdzXk4qX1tQcPYLPEVEQlRnj5+HNh7i18/vo76tm7mFmXx1fh6Fo0Jk0bmvG/Y/58LWrieguwUS0qFokZtGzLkYIrSE41z1d8B6FPgesBKYFQxY3wSw1v4g+JingW9ba9ef6bkUsMJDjz/A3zYd5hfP7qW6uZPLJqdzx4J8pmenel2aiMg58fkDPLr5MD9/di/Hmjq5dPIIvjo/n/Nyhntd2rvr6YC9a1zY2v0U+DogaZRrZlpyM4yd9Z6bUIvTbwHLGLMQuNpa+yVjTAUnA9avgA3W2geCj/s98KS19tHTPMftwO0AOTk5MysrK993PTK4dPb4eWBDJb95YT8Nbd3ML8rkq/Pz1UNLREJeIGB5bPtRfrZ2Lwfr2piencrXFuRz6eR0r0s7N12tsOcpKFvuQpe/C1JyoDgYtkZNU9g6g14FLGPMWiDrNHfdBXwLmG+tbXpHwPo1sP4dAesJa+3SM72WRrDCU2uXj/tePsj/rTtAS5ePa0uy+Jc5kykeneJ1aSIib+PzB3hs+1F+/fx+9h1vpSAriTvm53N14RBYU9rZ5KYPy5a56cSAD9ImQvESF7Yyi7yuMOT0ywiWMWYK8CzQHjw0FjiKW3f1SdAUoZybE23d3PfKQf74SgUtXT7mFo7kX+bkaupQRDzX4w+wfMsRfvPCPirq28nPTOJf5kweuldFtze4hfGlS6HiJbAByCgIhq0lkJ7rdYUhYUDaNLxjBKsYeIiTi9yfBXK1yF3ORlNHD396tYL7XjlIY3sPl+em88Wrczl/vLaDEJGB1eXz87dNh/mfF/ZzpLGDkjHJfGFOLvMKM4dmsDqd1uOu5UPpMjj0qjuWNcWNahXfBMPHe1qelwY8YAU/vwv4FOADvmytffK9nkMBS07V2uXjgQ2V/O6lA9S1dnPhhDS+eHUul0waMfiH4kUkpHV0+/nLa4f433X7qWnuYkZOKl+ck8uV+Rnh/fOn6QiUr3Bh60jw9/WYWW5Uq2gxpIzxtr4BpkajMqh1dPt56LVD/O+L+zne0sV5Oal84epcrswL8x90ItLn2oJv7P5Pb+ze24kKtzi+dBlUb3fHci4Jhq1FMGykp+UNBAUsGRI6e/z8bfNhfhscqi/ISuL22RO5YepoYqLUv0VE3r/jzZ388dUKHthQSXOnj8tz0/nCnFwumKClCWelbp9bHF+6DGp3gomA8Ze7sFW4EBKG5r+jApYMKd2+ACu3HuH/XjrAnppWMpNj+eSlE7j1ghxS4qO9Lk9EBpHd1S387qUDrNh6BH/Ack1JFp++fCIzQrmPVairKT8Zthr2Q0SU26KnZInbsidu6FwhroAlQ5K1lhf31PJ/Lx3glX31JMZE8uELcvjkpeMZOzzB6/JEJERZa3l1fz33rjvAi3tqiY+O5JZZY/nUZRMYN8KDLW2GKmvd1GHpUihdDk2HIDLGbT5dsgTyroHYYV5X2SsKWDLklR5p4ncvHeCx7ccAuH7KKD59+USmjB0675REpHd6/AEe336Me9cdoPxYM+nDYvnHS8bx0QvHMTxRGyD3K2vhyGYXtsqWQ8sxiIqHvAUubOXOh+h4r6s8ZwpYEjaONnbwx1creGjjIVq7fFw0MY3bLpvInIKRRIbLJdUi8jaN7d08sqmKP7xSwbGmTiaPHMbtl09k4fTRxEVHel1e+AkE4NB6N41YtgLa6yBmGORf58LWpDkQFet1lWdFAUvCTnNnDw+/VsV9rxzkWFMnY1Lj+ehFOXxoVjYjhg2Ob1wR6Z3SI03cv76ClVuP0uULcNHEND4zexJX5GWETw+rUOf3uUampUtdY9PORrdGq+BGF7YmXAGRUV5X+a4UsCRs9fgDrC2v4f71law/UE9MVAQ3TBnFxy8Zrw7xIkNQl8/PEzuOcf/6St441Eh8dCSLZ4zh4xePo3BUstflyZn4uuHAC25ka+dq6G6BhBHuKsSSm2HcJRARWiOOClgiwN6aFv68oZKlmw/T1u1n6tgU/uGicdw4TdMEIoPdkcYOHtxQycOvV1Hf1s3E9EQ+dtE4bp45VlcXD0Y9nbBvrQtbu5+EnnYYlumamZbcDGPPhwjv2/MoYImcoqWzhxVvHOH+9ZXsPd5KakI0H5qVzUcvHEfOCF19KDJYBAKWV/bXcf/6Sp7dWQPA1YWZfPzicVw6KV3TgENFdxvsedqFrT3PgL8LksdCyU1ub8TRM8CjJrAKWCKnYa1lw4EG/ryhgqfLavAHLJdOHsEts7JZUJylUS2REHWksYOlmw/zt81VVDV0MCIxhg+dn81HLxrHmNTBdyWanIPOZjeiVbYM9j0LgR4YPsGt1ypeApnFAxq2FLBE3kN1Uyd/21TFI8Ef2ElxUSyaPppbZmUzZUyKtsgQ8Vhnj5815TU8sqmKl/fVYS1vvSG6piSL2Ci9IQo7HSfcWq3SpXBwHVg/pOcFN6FeAhl5/V6CApbIWQoELBsO1vO3TYd5YscxunwBCrKS+OCsbBZPH60rEEUGWNnRJh55vYoVW4/S1NHDmNR4PjBzLB+YOZbsNE3pS1BrLexc6RqaVr4CWCi4AT78YL++rAKWyPvQ3NnDY9uO8simw2yraiQ60jC3MJNbZmVzeW46UZHeL7AUGYpOtHWzattRHtlURdnRZmKiIlhQnMUts8ZqbZW8t+ZjUL4CYhLhvI/360spYIn00u7qFh7ZVMXyN47Q0NbNiMQYrpsyikXTR3NeznD9wBfppbYuH2vKa1i17Sjr9tTiC1hKxiRzy6xsFk4bTWqCOq1L6FHAEukj3b4Az+06zmPbjrJ2Zw1dvgBjUuO5YdooFk4bTdGoZK3XEjlLXT4/L+6uZVXw+6mzJ8ColDhunDaaRdNHUzxaW11JaFPAEukHrV0+1pRXs2rrUV7aW4cvYJmUkcjCaWNYOH00E9K1aazIO/kDlvX761m17QhPlVbT3OkjLTGG66ZksXDaGGaN04iwDB4KWCL9rKGtmydLj7Fq61Feq2jAWpg6NoXrp4xiQXEW4xW2JIz5/AFerzjB02XVrN5+jLrWLobFRjG/OJOF00Zz6eR0orWmUQYhBSyRAXSsqYPHtx9j1bajbD/cBEBe5jDmF2WxoDiLkjGaRpShr6Pbz7q9tTxTVsOzu2pobO8hNiqCOQUjWThtNFcVjFSvORn0FLBEPHL4RDtrymt4pqyG1yoa8Acso1LimF+UyfziLC6YkKZ37jJknGjr5tldx3mmrJp1e2vp7AmQEh/N1QUjmV+cyey8DBJiQnfjXpFzpYAlEgLO9MtnXlEml+amkxynPdNkcKmoa+P53cdP+yZiQXEW5+tNhAxhClgiIeZ00yeREYbzclKZnZvB7LwMpoxJ0WJfCTmtXT7W769n3Z5a1u2tpbK+HdA0uIQnBSyREObzB9hceYJ1e2tZt6eOHUfcuq20xBgum5zO7LwMZuemMzI5zuNKJRwFApbyY83B/5+1bK48QY/fkhATycUTRzA7L4Mr8jJ0IYeEJQUskUGkrrWLl/fWBUcI6qhr7QKgICuJK/IzuGRSOjPHDWdYrNaySP84fKKdjQcaeGVfHev21lLX2g1A4ahkZuelc0VuBjPHD9f+fxL2FLBEBql3jh5sqjiBL2CJjDCUjE7mgglpXDBhBBeMTyMlQeu35NxZa6mob2fjgXpeO9jAxoMNHGnsAGB4QjSXB6esNYoq8vcUsESGiLYuH1sOnXjrF+HWqka6fQGMgfzMJC6aOCIYutJI18bUchqBgGVfbSsbD9Sz8WADrx1s4HiLGyUdkRjDhRPTuGC8C+4FWUlaByhyBgpYIkNUZ4+fbVWNbwWuzZUn6OjxAzAhPZFpY1OYOjaVadmpFI9OVt+hMFTb0sX2w41sq2pk2+Emth1upLG9B4Cs5DgunJjGhRNcMJ+UkajF6SLnoF8DljHmC8C/AD7gcWvtncHj3wRuA/zAF621T7/XcylgifROjz9A6ZEmNh5sYEvlCbYfbqK6uROAqAhDflaSC1xjU5iWnUruyGFE6RL6IaOls4cdR5rYVtXE9sONbD/c9NZ0X4SBvMwkpo1NZdb44Vw4YQTZafEKVCK9cKaA1atVssaYq4BFwFRrbZcxZmTweBHwYaAYGA2sNcbkWWv9vXk9ETmz6MgIZuQMZ0bO8LeO1TR3BkcvGtlW1cTq7Uf5y2uHAIiPjqR4dDIFo5LIz0wiPyuZ/MwkrecKcYGA5UhjB7urW9hd08Lu6hbKjzWzv7aVN98z56QlMCMnlU9eOv6tEUw1+RQZOL39bvtn4IfW2i4Aa+3x4PFFwF+Dxw8aY/YBFwDre/l6InKOMpPjmF+cxfziLMD9cq6ob2P74Sa2VjVSeqSJlW8cpaXL99bXZCXHkZ+VREFWEnmZSeRnJTF55DBNMXqgoa2bXdXN7K5uYU9NC7uqW9hT3UJb98n3q2NS48nPSuLGqaOZlu2mhdMSYzysWkR6G7DygMuNMXcDncAd1trXgTHAhlMedzh47O8YY24HbgfIycnpZTki8l4iIgwTM4YxMWMYi2e4b0trLceaOt82IrK7uoX1++vp9gfc1xkYMzye8SMSGTcigXFpwY8jEslJSyA+RuHr/bDWcqK9h4r6Nirr26isb6eyvp2K+jYO1bdT39b91mNTE6LJz0ziAzPHkhcMwLmZSdoBQCQEvWfAMsasBbJOc9ddwa8fDlwEnA88YoyZCJxuUv+0i72stfcC94Jbg3V2ZYtIXzLGMDo1ntGp8VxVMPKt4z5/gIr69reCV0WdCwGrtx97a6H0m7KS48gZkcD4EQmMHZ5AVnIcmSlxZCW7W3J8VFiu9/H5A9S1dlPd3ElN8HasqZNDDe0uUNW1v2300BgYnRLPuBEJzC/OYlJGIvlZbgo3Iyk2LP8NRQaj9wxY1tq573afMeafgWXWrZR/zRgTANJxI1bZpzx0LHC0l7WKyACLioxg8shhTB45jOsZ9bb7Gtu73WhLQzuVdW1U1LdzqKGN53fXUhu87P9UcdERZCbHvXXLSo4lMzmO1IQYUuOjSU1wt+T4aFLjY4iJCs3F99Za2rv9NHb00NjeTVN7D00dPTR29NDQ1k11U+fbwlRtSxeBd7x1jIowZKclkJOWwMyc4YwbcXI0MDstXg08RYaA3k4RrgDmAC8YY/KAGKAOWAU8ZIy5B7fIPRd4rZevJSIhJDUhhtSEGKZlp/7dfZ09fmpbuqhu7qS66WTYqG7uoqbJLbp/urmTbl/gXZ8/ISaS1PhoUhJiSImPIjEmirjoSGKjI4iLjiQuKpK46Ahigx/jot3H6MgIzmaQJxCALl+Azh4/nT4/nT0Bunr8dPb4Tx7vCdDp89PS6XNhqsNHU0c3Pf53H2xPiY9+a/QuPzOJrJQ3A2UcWSlxjEyOJT0xVv2lRIa43gas+4D7jDGlQDfwieBoVpkx5hGgHNe+4fO6glAkfMRFR5KdlkB2WsK7PsZaS3OHj8aObjcC1O5GgZrau0/+OXi8qaObY02ddL0ZhIIfO3v8+N45PNQLMVERxEW9GdZOBrikuCjys5JIiY9xI23x0aQER93eOpYQzfCEGF0IICJALwOWtbYb+Ni73Hc3cHdvnl9Ehi5jDCkJ0b1uCeHzB+j0BUeffAF6zjAq9vbX522jXzGRERpVEpE+o6YoIjKoRUVGMCwyQptfi0hICc1VpCIiIiKDmAKWiIiISB9TwBIRERHpY73e7LkvGWNqgcoBeKl0XDsJCT06N6FN5yd06dyENp2f0NWbczPOWptxujtCKmANFGPMpnfb/Vq8pXMT2nR+QpfOTWjT+Qld/XVuNEUoIiIi0scUsERERET6WLgGrHu9LkDelc5NaNP5CV06N6FN5yd09cu5Ccs1WCIiIiL9KVxHsERERET6jQKWiIiISB8Lq4BljLnGGLPbGLPPGPMNr+sJd8aY+4wxx40xpaccSzPGrDHG7A1+HO5ljeHKGJNtjHneGLPTGFNmjPlS8LjOTwgwxsQZY14zxmwLnp/vBI/r/IQIY0ykMeYNY8zq4Oc6NyHCGFNhjNlhjNlqjNkUPNbn5ydsApYxJhL4NXAtUATcaowp8raqsPdH4Jp3HPsG8Ky1Nhd4Nvi5DDwf8FVrbSFwEfD54PeLzk9o6ALmWGunAdOBa4wxF6HzE0q+BOw85XOdm9BylbV2+in9r/r8/IRNwAIuAPZZaw9Ya7uBvwKLPK4prFlr1wEN7zi8CPhT8M9/AhYPaFECgLX2mLV2S/DPLbhfFGPQ+QkJ1mkNfhodvFl0fkKCMWYscD3wu1MO69yEtj4/P+EUsMYAVad8fjh4TEJLprX2GLhf8sBIj+sJe8aY8cAMYCM6PyEjOAW1FTgOrLHW6vyEjp8BdwKBU47p3IQOCzxjjNlsjLk9eKzPz09Ub59gEDGnOaYeFSJnYIwZBiwFvmytbTbmdN9G4gVrrR+YboxJBZYbY0q8rknAGHMDcNxau9kYc6XX9chpXWqtPWqMGQmsMcbs6o8XCacRrMNA9imfjwWOelSLvLsaY8wogODH4x7XE7aMMdG4cPWgtXZZ8LDOT4ix1jYCL+DWM+r8eO9SYKExpgK3FGWOMeYBdG5ChrX2aPDjcWA5bglRn5+fcApYrwO5xpgJxpgY4MPAKo9rkr+3CvhE8M+fAFZ6WEvYMm6o6vfATmvtPafcpfMTAowxGcGRK4wx8cBcYBc6P56z1n7TWjvWWjse93vmOWvtx9C5CQnGmERjTNKbfwbmA6X0w/kJq07uxpjrcHPjkcB91tq7PS4prBlj/gJcCaQDNcB/ACuAR4Ac4BDwQWvtOxfCSz8zxlwGvATs4OQ6km/h1mHp/HjMGDMVtxA3EvdG+RFr7XeNMSPQ+QkZwSnCO6y1N+jchAZjzETcqBW4ZVIPWWvv7o/zE1YBS0RERGQghNMUoYiIiMiAUMASERER6WMKWCIiIiJ9TAFLREREpI8pYImIiIj0MQUsERERkT6mgCUiIiLSx/4/5GYAHYwucX8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot([0]*len(x),color=\"k\")\n",
    "plt.plot(-M)\n",
    "plt.ylim(top=(q*1/2)+50)\n",
    "plt.plot(V)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2. 6.] -2.6043167622447072e-11\n",
      "    fjac: array([[-0.99510594,  0.09881382],\n",
      "       [-0.09881382, -0.99510594]])\n",
      "     fun: array([-2.60431676e-11,  9.94049287e-12])\n",
      " message: 'The solution converged.'\n",
      "    nfev: 14\n",
      "     qtf: array([ 5.01576515e-08, -1.36480021e-08])\n",
      "       r: array([ 5.43312215, -3.40464439, -2.94653327])\n",
      "  status: 1\n",
      " success: True\n",
      "       x: array([2., 6.]) -2.6043167622447072e-11\n",
      "1.9999999999999998 6.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(*args, **kw)>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import fsolve,root,leastsq\n",
    "l=5\n",
    "q=20\n",
    "x=np.linspace(0,10,500)\n",
    "y1=-x*x+16*x\n",
    "y2=x*x-8*x+12\n",
    "def poly(x):\n",
    "    err=x*x-8*x+12\n",
    "    return err   \n",
    "func=lambda x : x*x-8*x+12\n",
    "result=fsolve(func,[0,10])\n",
    "result1=root(poly,[0,10],method='hybr')\n",
    "result2=leastsq(poly,[0,10])\n",
    "\n",
    "  \n",
    "print(result,poly(result[0]))\n",
    "print(result1,poly(result1[\"x\"][0]))\n",
    "print(result2[0][0],result2[0][1])\n",
    "  \n",
    "#plt.plot(y1)\n",
    "plt.plot(x,y2)\n",
    "plt.plot(x,0*x)\n",
    "xy=(result1[\"x\"][0],poly(result1[\"x\"][0]))\n",
    "plt.annotate('Root1',xy,xytext=(3,6),\n",
    "             arrowprops=dict(facecolor='red',shrink=0.05))\n",
    "xy=(result1[\"x\"][1],poly(result1[\"x\"][1]))\n",
    "plt.annotate('Root2',xy,xytext=(5,6),\n",
    "             arrowprops=dict(facecolor='red',shrink=0.05))\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "module 'matplotlib.pyplot' has no attribute 'axline'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-7-78a275bcae62>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maxhline\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"black\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlinestyle\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"--\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maxvline\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcolor\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"grey\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 8\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maxline\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mslope\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0.25\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"black\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlinestyle\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      9\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msig\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlinewidth\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34mr\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     10\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxlim\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: module 'matplotlib.pyplot' has no attribute 'axline'"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-10, 10, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "\n",
    "plt.axhline(y=0, color=\"black\", linestyle=\"--\")\n",
    "plt.axhline(y=0.5, color=\"black\", linestyle=\":\")\n",
    "plt.axhline(y=1.0, color=\"black\", linestyle=\"--\")\n",
    "plt.axvline(color=\"grey\")\n",
    "plt.axline((0, 0.5), slope=0.25, color=\"black\", linestyle=(0, (5, 5)))\n",
    "plt.plot(t, sig, linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
    "plt.xlim(-10, 10)\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
